Recent years have witnessed significant progress in a variety of emerging areas including meta-learning and fine-tuning [11, 52], automated hyperparameter optimization [13, 10], reinforcement learning [31, 21], fair batch selection in machine learning [54], adversarial learning [76, 40], AI-aware communication networks [27], fairness-aware federated learning [75], etc. These problems share a common nested optimization structure, and have inspired intensive study on the theory and algorithmic development of bilevel optimization. Prior efforts have been taken mainly on the single-machine scenario. However, in modern machine learning applications, data privacy has emerged as a critical concern in centralized training, and the data often exhibit an inherently distributed nature [70]. This highlights the importance of recent research and attention on federated bilevel optimization, and has inspired many emerging applications including but not limited to federated meta-learning [9], hyperparameter tuning for federated learning [25], resource allocation over communication networks [27] and graph-aided federated learning [71], adversarial robustness on edge computing [46], etc.

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of normal distributions by a finite mixture of normal distributions; and (ii) the use of variational approximations to efficiently estimate prior hyperparameters and compute approximate posteriors. Combining these two ideas results in fast and flexible methods, with computational speed comparable to fast penalized regression methods such as the Lasso, and with competitive prediction accuracy across a wide range of scenarios. Further, we provide new results that establish conceptual connections between our empirical Bayes methods and penalized methods. Specifically, we show that the posterior mean from our method solves a penalized regression problem, with the form of the penalty function being learned from the data by directly solving an optimization problem (rather than being tuned by cross-validation). Our methods are implemented in an R package, mr.ash.alpha,

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywise calibrated intervals for future samples of any diffusion model, and $(ii)$ control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

We study a Stackelberg game between an attacker and a defender on large Active Directory (AD) attack graphs where the defender employs a set of honeypots to stop the attacker from reaching high-value targets. Contrary to existing works that focus on small and static attack graphs, AD graphs typically contain hundreds of thousands of nodes and edges and constantly change over time. We consider two types of attackers: a simple attacker who cannot observe honeypots and a competent attacker who can. To jointly solve the game, we propose a mixed-integer programming (MIP) formulation. We observed that the optimal blocking plan for static graphs performs poorly in dynamic graphs. To solve the dynamic graph problem, we re-design the mixed-integer programming formulation by combining m MIP (dyMIP(m)) instances to produce a near-optimal blocking plan. Furthermore, to handle a large number of dynamic graph instances, we use a clustering algorithm to efficiently find the m-most representative graph instances for a constant m (dyMIP(m)). We prove a lower bound on the optimal blocking strategy for dynamic graphs and show that our dyMIP(m) algorithms produce close to optimal results for a range of AD graphs under realistic conditions.

A wide array of modern machine learning applications - from adversarial models to multi-agent reinforcement learning - can be formulated as non-cooperative games whose Nash equilibria represent the system's desired operational states. Despite having a highly non-convex loss landscape, many cases of interest possess a latent convex structure that could potentially be leveraged to yield convergence to an equilibrium. Driven by this observation, our paper proposes a flexible first-order method that successfully exploits such "hidden structures" and achieves convergence under minimal assumptions for the transformation connecting the players' control variables to the game's latent, convex-structured layer. The proposed method - which we call preconditioned hidden gradient descent (PHGD) - hinges on a judiciously chosen gradient preconditioning scheme related to natural gradient methods. Importantly, we make no separability assumptions for the game's hidden structure, and we provide explicit convergence rate guarantees for both deterministic and stochastic environments.

Existing methods provide varying algorithms for different types of Boolean satisfiability problems (SAT), lacking a general solution framework. Accordingly, this study proposes a unified framework DCSAT based on integer programming and reinforcement learning (RL) algorithm to solve different types of SAT problems such as MaxSAT, Weighted MaxSAT, PMS, WPMS. Specifically, we first construct a consolidated integer programming representation for four types of SAT problems by adjusting objective function coefficients. Secondly, we construct an appropriate reinforcement learning models based on the 0-1 integer programming for SAT problems. Based on the binary tree search structure, we apply the Monte Carlo tree search (MCTS) method on SAT problems. Finally, we prove that this method can find all optimal Boolean assignments based on Wiener-khinchin law of large Numbers. We experimentally verify that this paradigm can prune the unnecessary search space to find the optimal Boolean assignments for the problem. Furthermore, the proposed method can provide diverse labels for supervised learning methods for SAT problems.

This paper introduces an extension to the Orienteering Problem (OP), called Clustered Orienteering Problem with Subgroups (COPS). In this variant, nodes are arranged into subgroups, and the subgroups are organized into clusters. A reward is associated with each subgroup and is gained only if all of its nodes are visited; however, at most one subgroup can be visited per cluster. The objective is to maximize the total collected reward while attaining a travel budget. We show that our new formulation has the ability to model and solve two previous well-known variants, the Clustered Orienteering Problem (COP) and the Set Orienteering Problem (SOP), in addition to other scenarios introduced here. An Integer Linear Programming (ILP) formulation and a Tabu Search-based heuristic are proposed to solve the problem. Experimental results indicate that the ILP method can yield optimal solutions at the cost of time, whereas the metaheuristic produces comparable solutions within a more reasonable computational cost.

Multi-Task Learning (MTL) involves developing a singular model, known as a multi-task model, to concurrently perform multiple tasks. While the security of single-task models has been thoroughly studied, multi-task models pose several critical security questions, such as 1) their vulnerability to single-task adversarial attacks, 2) the possibility of designing attacks that target multiple tasks, and 3) the impact of task sharing and adversarial training on their resilience to such attacks. This paper addresses these queries through detailed analysis and rigorous experimentation. First, we explore the adaptation of single-task white-box attacks to multi-task models and identify their limitations. We then introduce a novel attack framework, the Gradient Balancing Multi-Task Attack (GB-MTA), which treats attacking a multi-task model as an optimization problem. This problem, based on averaged relative loss change across tasks, is approximated as an integer linear programming problem. Extensive evaluations on MTL benchmarks, NYUv2 and Tiny-Taxonomy, demonstrate GB-MTA's effectiveness against both standard and adversarially trained multi-task models. The results also highlight a trade-off between task accuracy improvement via parameter sharing and increased model vulnerability due to enhanced attack transferability.

Discontinuities can be fairly arbitrary but also cause a significant impact on outcomes in larger systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression discontinuity from econometrics assumes the existence of a discontinuous variable that splits the population into distinct partitions to estimate the causal effects of a given phenomenon. Here we consider the design of partitions for a given discontinuous variable to optimize a certain effect previously studied using regression discontinuity. To do so, we propose a quantization-theoretic approach to optimize the effect of interest, first learning the causal effect size of a given discontinuous variable and then applying dynamic programming for optimal quantization design of discontinuities to balance the gain and loss in that effect size. We also develop a computationally-efficient reinforcement learning algorithm for the dynamic programming formulation of optimal quantization. We demonstrate our approach by designing optimal time zone borders for counterfactuals of social capital, social mobility, and health. This is based on regression discontinuity analyses we perform on novel data, which may be of independent empirical interest.

LiDAR-inertial odometry (LIO), which fuses complementary information of a LiDAR and an Inertial Measurement Unit (IMU), is an attractive solution for state estimation. In LIO, both pose and velocity are regarded as state variables that need to be solved. However, the widely-used Iterative Closest Point (ICP) algorithm can only provide constraint for pose, while the velocity can only be constrained by IMU pre-integration. As a result, the velocity estimates inclined to be updated accordingly with the pose results. In this paper, we propose LIWO, an accurate and robust LiDAR-inertialwheel (LIW) odometry, which fuses the measurements from LiDAR, IMU and wheel encoder in a bundle adjustment (BA) based optimization framework. The involvement of a wheel encoder could provide velocity measurement as an important observation, which assists LIO to provide a more accurate state prediction. In addition, constraining the velocity variable by the observation from wheel encoder in optimization can further improve the accuracy of state estimation. Experiment results on two public datasets demonstrate that our system outperforms all state-of-the-art LIO systems in terms of smaller absolute trajectory error (ATE), and embedding a wheel encoder can greatly improve the performance of LIO based on the BA framework.